I haven't been to Yellowstone is several years. When I went to Yellowstone I saw sheep close to the north
entrance/exit (the exit to Gardiner Montana) and these were seen from the road.
No help on the rest of your route.
I just saw some in the Badlands south of Wall S.D. a week ago, along with plenty of Bison. That Badlands loop is a great drive. Saw some Mt. Goats near Mt. Rushmore a few years ago. Right in the ditch next to the road.